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Consider a network of four processors that use the Oral Messages (Byzantine Generals) algorithm of Pease, Shostak and Lamport to achieve agreement in the presence of faults. Bevier and Young have published a functional description of a single processor that, when interconnected appropriately with three identical others, implements this network under the assumption that the four processors step in synchrony. By formalizing the original Pease, Shostak and Lamport work, Bevier and Young mechanically proved that such a network achieves fault tolerance. In this paper we develop, formalize and discuss a hardware design that has been mechanically proved to implement their processor. In particular, we formally define mapping functions from the abstract state space of the Bevier-Young processor to a concrete state space of a hardware module and state a theorem that expresses the claim that the hardware correctly implements the processor. We briefly discuss the Brock-Hunt Formal Hardware Descrip..

CFD ANALYSIS, SENSITIVITY ANALYSIS, AND DESIGN CODES IN MDO

Observations regarding the use of advanced computational #uid dynamics #CFD# analysis, sensitivity analysis #SA#, and design codes in gradient-based multidisciplinary design optimization #MDO# re#ect our perception of the interactions required of CFD and our experience in recent aerodynamic design optimization studies using CFD. Sample results from these latter studies are summarized for conventional optimization #analysis-SA codes# and simultaneous analysis and design optimization #design code# using both Euler and NavierStokes #ow approximations. The SA codes is greater than that required for design codes